Diffusively-Coupled Rock-Paper-Scissors Game with Mutation in Scale-Free Hierarchical Networks
We present a metapopulation dynamic model for the diffusively-coupled rock-paper-scissors (RPS) game with mutation in scale-free hierarchical networks. We investigate how the RPS game changes by mutation in scale-free networks. Only the mutation from rock to scissors (R-to-S) occurs with rate μ. In...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/6976328 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832550088436613120 |
|---|---|
| author | Takashi Nagatani Genki Ichinose |
| author_facet | Takashi Nagatani Genki Ichinose |
| author_sort | Takashi Nagatani |
| collection | DOAJ |
| description | We present a metapopulation dynamic model for the diffusively-coupled rock-paper-scissors (RPS) game with mutation in scale-free hierarchical networks. We investigate how the RPS game changes by mutation in scale-free networks. Only the mutation from rock to scissors (R-to-S) occurs with rate μ. In the network, a node represents a patch where the RPS game is performed. RPS individuals migrate among nodes by diffusion. The dynamics are represented by the reaction-diffusion equations with the recursion formula. We study where and how species coexist or go extinct in the scale-free network. We numerically obtained the solutions for the metapopulation dynamics and derived the transition points. The results show that, with increasing mutation rate μ, the extinction of P species occurs and then the extinction of R species occurs, and finally only S species survives. Thus, the first and second dynamical phase transitions occur in the scale-free hierarchical network. We also show that the scaling law holds for the population dynamics which suggests that the transition points approach zero in the limit of infinite size. |
| format | Article |
| id | doaj-art-98f2aed33fee4608a05b13b86d466e8f |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-98f2aed33fee4608a05b13b86d466e8f2025-02-03T06:07:41ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/69763286976328Diffusively-Coupled Rock-Paper-Scissors Game with Mutation in Scale-Free Hierarchical NetworksTakashi Nagatani0Genki Ichinose1Department of Mechanical Engineering, Shizuoka University, Hamamatsu 432-8561, JapanDepartment of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu 432-8561, JapanWe present a metapopulation dynamic model for the diffusively-coupled rock-paper-scissors (RPS) game with mutation in scale-free hierarchical networks. We investigate how the RPS game changes by mutation in scale-free networks. Only the mutation from rock to scissors (R-to-S) occurs with rate μ. In the network, a node represents a patch where the RPS game is performed. RPS individuals migrate among nodes by diffusion. The dynamics are represented by the reaction-diffusion equations with the recursion formula. We study where and how species coexist or go extinct in the scale-free network. We numerically obtained the solutions for the metapopulation dynamics and derived the transition points. The results show that, with increasing mutation rate μ, the extinction of P species occurs and then the extinction of R species occurs, and finally only S species survives. Thus, the first and second dynamical phase transitions occur in the scale-free hierarchical network. We also show that the scaling law holds for the population dynamics which suggests that the transition points approach zero in the limit of infinite size.http://dx.doi.org/10.1155/2020/6976328 |
| spellingShingle | Takashi Nagatani Genki Ichinose Diffusively-Coupled Rock-Paper-Scissors Game with Mutation in Scale-Free Hierarchical Networks Complexity |
| title | Diffusively-Coupled Rock-Paper-Scissors Game with Mutation in Scale-Free Hierarchical Networks |
| title_full | Diffusively-Coupled Rock-Paper-Scissors Game with Mutation in Scale-Free Hierarchical Networks |
| title_fullStr | Diffusively-Coupled Rock-Paper-Scissors Game with Mutation in Scale-Free Hierarchical Networks |
| title_full_unstemmed | Diffusively-Coupled Rock-Paper-Scissors Game with Mutation in Scale-Free Hierarchical Networks |
| title_short | Diffusively-Coupled Rock-Paper-Scissors Game with Mutation in Scale-Free Hierarchical Networks |
| title_sort | diffusively coupled rock paper scissors game with mutation in scale free hierarchical networks |
| url | http://dx.doi.org/10.1155/2020/6976328 |
| work_keys_str_mv | AT takashinagatani diffusivelycoupledrockpaperscissorsgamewithmutationinscalefreehierarchicalnetworks AT genkiichinose diffusivelycoupledrockpaperscissorsgamewithmutationinscalefreehierarchicalnetworks |